Hi I'm redoing my bathtub surround (because I did it incorrectly the first time). Basically there is only 3" between the tub and the door frame. How much should I extend the tile past the tub? How thin should my door frame be? If I install the door frame this close to the tub should I use special wood proof material (all the trim I currently have is MDF but I've heard that's bad to use in wet areas).
I think I'd run the tile all the way out over the door frame. You definitely don't want to do mdf trim there. Go with natural wood, or one of the synthetic materials.
I have seen the tile and trim done a few different ways. There are two ways I prefer, but only one of the two ways would work in your situation. That is to stop the tile on top of the tub and not bring it down the side of the tub. This would give you the full 3" for the trim. If your trim will be the standard 2 1/4" that is used a lot these days, this arrangement will give room so the trim and tile do not compete for the space. Also I have cut tile to meet the trim, but never cut or ripped trim to meet tile. It would make it look incomplete in my opinion if that was done, depending on the style of trim which has not been mentioned.
The painting of the backside of the trim as mentioned by Kelly, is a good way to combat the water that may get on the trim. It is a lot less than you may think, unless somebody simply does not use a shower curtain properly. But never-the-less I would paint the front, back, sides and especially the bottom where it meets the floor with an oil based paint, water based allows moisture to pass through. You could prime 2 coats with oil based and finish it with the latex (water based) of your choice.
I would not sweat the difference in thickness the paint builds up to, there are other factors the make the joints not line up as expected as it is. It is all part of installing trim.
The tile is really up to you and what looks best to you. As for the door frame, you can buy a moisture resistant trim, which is not expensive, and paint it with moisture resistant paint. I would recommend you paint the trim on both front and back and with a couple of coats.
I would use vinyl trim such as https://www.homedepot.com/p/Veranda-White-Vinyl-Prefinished-Trim-Kit-2-Piece-0201/202033621
Regarding that 3" area, what Jack suggested would give you the best look in my opinion.